Measurements and Geometry

Area of Polygons - Area of parallelograms and rhombus

By the end of the lesson, the learner should be able to:
- Determine the area of parallelograms using A = ab sin θ
- Determine the area of a rhombus using A = a² sin θ
- Apply the formulae to real-life objects such as cloth pieces, tiles and parking lots

In groups, learners are guided to:
- Consider a parallelogram divided into two equal triangles and derive the area formula
- Work out the area of parallelograms and rhombuses using the sine of included angles

How do we work out the area of polygons?

- Master Core Mathematics Grade 10 pg. 149
- Rulers and geometrical set
- Scientific calculators
- Mathematical tables

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of Polygons - Area of trapeziums and kites
Area of Polygons - Area of regular heptagon

By the end of the lesson, the learner should be able to:
- Determine the area of trapeziums using trigonometric methods
- Determine the area of kites by dividing into triangles
- Relate the area of trapeziums and kites to practical applications such as bridge supports and shutters

In groups, learners are guided to:
- Work out the area of trapeziums by finding the height using trigonometric ratios
- Divide kites into triangles and calculate the total area
- Solve problems involving real-life trapezoidal and kite shapes

How do we work out the area of polygons?

- Master Core Mathematics Grade 10 pg. 150
- Rulers and geometrical set
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 152
- Rulers, compasses and geometrical set
- Scientific calculators
- Protractors

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Area of regular octagon
Area of Polygons - Area of irregular polygons

By the end of the lesson, the learner should be able to:
- Work out the area of a regular octagon by dividing it into triangles from the centre
- Calculate the central angle and use the sine formula for triangles
- Apply the area of a regular octagon to real-life objects such as nut openers, bolt heads and floor tile patterns

In groups, learners are guided to:
- Draw a circle and divide the circumference into eight equal parts to form a regular octagon
- Join the vertices to the centre and calculate the area of each triangle formed
- Use the formula for area of a regular polygon

How do we apply the concept of the area of polygons in real-life situations?

- Master Core Mathematics Grade 10 pg. 155
- Rulers, compasses and geometrical set
- Scientific calculators
- Protractors
- Master Core Mathematics Grade 10 pg. 158
- Rulers and geometrical set
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of Polygons - Application of area of irregular polygons
Area of Polygons - Application of area of polygons to real-life situations
Area of a Part of a Circle - Area of an annulus

By the end of the lesson, the learner should be able to:
- Solve more complex problems involving irregular polygons
- Work out the area of polygons with multiple component shapes
- Apply the concept of area of irregular polygons to real-life situations such as land surveying and floor plan estimation

In groups, learners are guided to:
- Work out the areas of complex irregular polygons from various real-life contexts
- Research and discuss in a group the use of the area of polygons in real-life situations

How do we apply the concept of the area of polygons in real-life situations?

- Master Core Mathematics Grade 10 pg. 159
- Rulers and geometrical set
- Scientific calculators
- Digital resources
- Mathematical tables
- Master Core Mathematics Grade 10 pg. 161
- Circular objects
- Compasses
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Area of a sector of a circle
Area of a Part of a Circle - Area of an annular sector

By the end of the lesson, the learner should be able to:
- Work out the area of a sector of a circle
- Apply the formula Area = (θ/360) × πr²
- Relate the area of a sector to real-life situations such as area swept by a clock hand, paper fans and garden gates

In groups, learners are guided to:
- Work in a group and use paper cutouts to make sectors of circles to determine their areas
- Calculate the area of sectors using the formula

How do we use the concept of the area of a part of a circle in real life?

- Master Core Mathematics Grade 10 pg. 163
- Compasses and protractors
- Paper cutouts
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 166
- Rulers

- Observation - Oral questions - Written assignments

Measurements and Geometry

Area of a Part of a Circle - Application of area of an annular sector
Area of a Part of a Circle - Area of a segment of a circle
Area of a Part of a Circle - Application of area of a segment

By the end of the lesson, the learner should be able to:
- Solve more problems involving the area of an annular sector
- Apply the concept to various real-life contexts
- Use annular sector area in practical problems such as assembly grounds, brake pads and dart boards

In groups, learners are guided to:
- Work out more examples involving area of annular sectors
- Solve problems related to annular sectors from real-life situations

How do we use the concept of the area of a part of a circle in real life?

- Master Core Mathematics Grade 10 pg. 167
- Scientific calculators
- Rulers
- Protractors
- Master Core Mathematics Grade 10 pg. 169
- Compasses and protractors
- Rulers and geometrical set
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 171

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Area of common region between two intersecting circles
Area of a Part of a Circle - Common region (finding radii and angles)

By the end of the lesson, the learner should be able to:
- Determine the area of the common region between two intersecting circles
- Identify the common area as the sum of two segments
- Relate intersecting circles to real-life situations such as overlapping lights and water sprinklers

In groups, learners are guided to:
- Draw two circles intersecting at two points
- Join the centres and the points of intersection
- Separate the common region into two segments and calculate the total area

How do we use the concept of the area of a part of a circle in real life?

- Master Core Mathematics Grade 10 pg. 173
- Compasses and rulers
- Scientific calculators
- Protractors
- Master Core Mathematics Grade 10 pg. 175
- Rulers and geometrical set

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Further problems on common region

By the end of the lesson, the learner should be able to:
- Solve further problems involving the area of the common region between two intersecting circles
- Work out problems involving overlapping circles with different radii
- Use the area of intersecting circles to solve practical problems such as planning water sprinkler coverage and designing logos

In groups, learners are guided to:
- Work out further problems on the area of the common region
- Use digital devices and other resources to learn more about the area of a part of a circle

How do we use the concept of the area of a part of a circle in real life?

- Master Core Mathematics Grade 10 pg. 177
- Scientific calculators
- Digital resources
- Rulers and geometrical set

- Observation - Oral questions - Written tests

Measurements and Geometry

Area of a Part of a Circle - Application to real-life situations
Surface Area and Volume of Solids - Surface area of prisms
Surface Area and Volume of Solids - Surface area of pyramids

By the end of the lesson, the learner should be able to:
- Apply the area of a part of a circle to solve mixed real-life problems
- Combine different concepts (annulus, sector, annular sector, segment, common region)
- Relate the area of a part of a circle to practical projects such as making dartboards and beaded necklaces

In groups, learners are guided to:
- Relate and work out the area of a part of a circle in real-life situations
- Make a dartboard of different numbers of concentric circles from locally available materials
- Discuss and create rules for scoring the game

How do we use the concept of the area of a part of a circle in real life?

- Master Core Mathematics Grade 10 pg. 177
- Locally available materials
- Scientific calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 179
- Models of prisms
- Scissors
- Rulers and geometrical set
- Master Core Mathematics Grade 10 pg. 184
- Models of pyramids
- Rulers and geometrical set
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Surface area of cones
Surface Area and Volume of Solids - Surface area of frustums

By the end of the lesson, the learner should be able to:
- Determine the surface area of cones
- Calculate the curved surface area and total surface area of a cone
- Apply surface area of cones to real-life objects such as paper cups, conical hats and tents

In groups, learners are guided to:
- Cut out the circular base and curved surface of a cone to form a net
- Calculate the surface area using Area = πr² + πrl
- Solve problems involving surface area of cones

How do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 186
- Models of cones
- Rulers and geometrical set
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 188
- Models of frustums

- Observation - Oral questions - Written assignments

Measurements and Geometry

Surface Area and Volume of Solids - Surface area of spheres and hemispheres
Surface Area and Volume of Solids - Surface area of composite solids
Surface Area and Volume of Solids - Volume of prisms

By the end of the lesson, the learner should be able to:
- Determine the surface area of spheres and hemispheres
- Apply the formulae SA = 4πr² (sphere) and SA = 3πr² (hemisphere)
- Relate surface area of spheres to real-life objects such as balls, chocolates and water tanks

In groups, learners are guided to:
- Collect spherical objects and measure their circumference
- Work out the radius and calculate the surface area
- Discuss how to work out the surface area of a hemisphere

How do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 191
- Spherical objects
- String and rulers
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 193
- Models of composite solids
- Rulers and geometrical set
- Master Core Mathematics Grade 10 pg. 196
- Models of prisms
- Rulers

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Volume of pyramids
Surface Area and Volume of Solids - Volume of cones

By the end of the lesson, the learner should be able to:
- Calculate the volume of pyramids (square-based, rectangular-based, pentagonal, hexagonal)
- Apply the formula Volume = ⅓ × Base area × Height
- Relate volume of pyramids to real-life objects such as roofs, monuments and milk packets

In groups, learners are guided to:
- Collect different models of pyramids and discuss how to work out the volume
- Calculate the base area and perpendicular height to determine the volume

Why do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 198
- Models of pyramids
- Rulers and geometrical set
- Scientific calculators
- Master Core Mathematics Grade 10 pg. 200
- Models of cones and cylinders
- Sand or water

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Volume of frustums

By the end of the lesson, the learner should be able to:
- Calculate the volume of frustums of cones and pyramids
- Extend slant heights to form the original solid and subtract the volume of the cut-off part
- Apply the volume of frustums to real-life objects such as buckets, water tanks and washing sinks

In groups, learners are guided to:
- Extend the slant heights of a frustum to obtain the original solid
- Calculate the volume of the original solid and the small solid cut off
- Subtract to get the volume of the frustum

How do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 201
- Models of frustums
- Rulers
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Volume of spheres and hemispheres

By the end of the lesson, the learner should be able to:
- Calculate the volume of spheres and hemispheres
- Apply the formulae V = ⁴⁄₃πr³ (sphere) and V = ²⁄₃πr³ (hemisphere)
- Relate volume of spheres to real-life objects such as balls, ornaments, bowls and water tanks

In groups, learners are guided to:
- Collect spherical objects and measure their circumference
- Work out the radius and calculate the volume
- Discuss and work out the volume of hemispheres

Why do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 204
- Spherical objects
- String and rulers
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Volume of composite solids

By the end of the lesson, the learner should be able to:
- Determine the volume of composite solids
- Identify the component shapes, calculate individual volumes and sum them
- Relate composite solids to real-life objects such as LPG tanks, silos and trophies

In groups, learners are guided to:
- Collect a model of a composite solid and identify all the basic shapes
- Work out the volume of each shape and add the volumes
- Solve problems involving composite solids

Why do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 206
- Models of composite solids
- Rulers
- Scientific calculators

- Observation - Oral questions - Written tests

Measurements and Geometry

Surface Area and Volume of Solids - Application to real-life situations
Vectors I - Vector and scalar quantities
Vectors I - Vector notation

By the end of the lesson, the learner should be able to:
- Apply surface area and volume of solids to solve mixed real-life problems
- Combine different formulae to solve problems involving various solids
- Use the concepts of surface area and volume in practical situations such as determining quantities of materials for construction, painting and storage capacity

In groups, learners are guided to:
- Use appropriate containers from the local environment to work out the volume and capacity
- Use digital devices and other resources to work out the surface area and volume of solids
- Solve combined problems involving surface area and volume

Why do we determine the surface area and volume of solids?

- Master Core Mathematics Grade 10 pg. 206
- Containers from the local environment
- Scientific calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 208
- Measuring tape
- Magnetic compass
- Stopwatch
- Master Core Mathematics Grade 10 pg. 209
- Charts
- Rulers

- Observation - Oral questions - Written tests

Measurements and Geometry

Vectors I - Representation of vectors
Vectors I - Equivalent vectors

By the end of the lesson, the learner should be able to:
- Represent vectors geometrically using directed line segments
- Draw vectors showing magnitude and direction on diagrams
- Connect vector representation to real-life navigation such as giving directions using landmarks and compass bearings

In groups, learners are guided to:
- Mark two points on the floor and walk from one to the other to demonstrate vector direction
- Draw vectors on plain paper and grids showing initial and terminal points
- Represent given vectors using diagrams and share work with peers

How do we represent the magnitude and direction of a vector on a diagram?

- Master Core Mathematics Grade 10 pg. 210
- Rulers
- Graph papers
- Charts
- Digital resources
- Master Core Mathematics Grade 10 pg. 211
- Charts showing cuboids

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Addition of vectors using head-to-tail method
Vectors I - Addition of vectors using parallelogram method

By the end of the lesson, the learner should be able to:
- Add vectors using the head-to-tail (triangle) method
- Draw the resultant vector from given component vectors on a grid
- Connect vector addition to real-life situations such as combining two flight paths or two forces acting on an object

In groups, learners are guided to:
- Draw vectors on a grid and place the tail of the second vector at the head of the first
- Draw the resultant vector from the tail of the first vector to the head of the second
- Illustrate sums of vectors on graph paper and share work with peers

How do we find the resultant of two or more vectors?

- Master Core Mathematics Grade 10 pg. 213
- Graph papers
- Rulers
- Geometrical set
- Digital resources
- Master Core Mathematics Grade 10 pg. 214

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Multiplication of vectors by scalar
Vectors I - Column vectors
Vectors I - Position vectors

By the end of the lesson, the learner should be able to:
- Multiply vectors by positive, negative and zero scalars
- Simplify expressions involving scalar multiplication of vectors
- Connect scalar multiplication to real-life situations such as doubling or tripling a journey's displacement or reversing direction

In groups, learners are guided to:
- Draw a vector on a graph paper and multiply its length by 2, -2 and 0
- Draw the new vectors and compare length and direction
- Simplify vector expressions involving scalar multiples and share work with peers

What happens to a vector when it is multiplied by a scalar?

- Master Core Mathematics Grade 10 pg. 216
- Graph papers
- Rulers
- Charts
- Digital resources
- Master Core Mathematics Grade 10 pg. 218
- Grids
- Master Core Mathematics Grade 10 pg. 221
- Geometrical set
- Calculators

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Magnitude of a vector and midpoint of a vector

By the end of the lesson, the learner should be able to:
- Determine the magnitude of a vector using the Pythagorean theorem
- Calculate the midpoint of a vector given coordinates of two points
- Relate magnitude and midpoint to real-life applications such as finding the straight-line distance between two towns or the halfway point of a journey

In groups, learners are guided to:
- Draw a right-angled triangle from a vector on a grid and use Pythagoras' theorem to find the magnitude
- Calculate magnitude of different vectors and determine midpoints of given vectors
- Solve problems involving magnitude and midpoint and share work with peers

How do we determine the length of a vector and the midpoint between two points?

- Master Core Mathematics Grade 10 pg. 224
- Graph papers
- Rulers
- Calculators
- Digital resources

- Oral questions - Observation - Written assignments

Measurements and Geometry

Vectors I - Translation vector

By the end of the lesson, the learner should be able to:
- Define and determine translation vectors as a transformation
- Find the image of a point or shape under a given translation
- Relate translation vectors to real-life movements such as sliding furniture across a room or shifting objects on a conveyor belt without rotating them

In groups, learners are guided to:
- Draw a Cartesian plane and place a triangular paper cutout, then slide it and record new coordinates
- Express the movement as a column vector and determine images of points under translation
- Draw objects and their images under translation on the same axes and share work

How do we use vectors to describe the movement of objects without turning?

- Master Core Mathematics Grade 10 pg. 227
- Graph papers
- Rulers
- Paper cutouts
- Geometrical set
- Digital resources

- Oral questions - Observation - Written assignments

Measurements and Geometry

Linear Motion - Distance, displacement, speed, velocity and acceleration
Linear Motion - Velocity
Linear Motion - Acceleration and deceleration

By the end of the lesson, the learner should be able to:
- Define the terms distance, displacement, speed, velocity and acceleration
- Differentiate between distance and displacement, and between speed and velocity
- Relate the terms to everyday experiences such as walking to school, road signposts showing distances to towns and vehicle speedometers

In groups, learners are guided to:
- Use a digital device or other sources to search for the meaning of the terms distance, displacement, speed, velocity and acceleration
- Explain the difference between distance and displacement, and between speed and velocity
- Identify real-life examples from road signs and share findings with peers

What is the difference between distance and displacement?

- Master Core Mathematics Grade 10 pg. 231
- Measuring tape
- Stopwatch
- Digital resources
- Master Core Mathematics Grade 10 pg. 232
- Rulers
- Toy car or marble
- Wooden plank
- Master Core Mathematics Grade 10 pg. 234
- Ball
- Ramp
- Calculators

- Oral questions - Observation - Written assignments

Measurements and Geometry

Linear Motion - Displacement-time graph
Linear Motion - Interpreting displacement-time graph

By the end of the lesson, the learner should be able to:
- Draw displacement-time graphs from given data tables
- Select suitable scales for axes when plotting graphs
- Connect displacement-time graphs to real-life journeys such as plotting an athlete's race or a cyclist's trip between towns

In groups, learners are guided to:
- Mark a straight track and walk at a steady pace, recording displacement at intervals
- Use data tables to plot displacement-time graphs on graph paper
- Draw displacement-time graphs for journeys involving stops and return trips and share work

How do we represent a journey using a displacement-time graph?

- Master Core Mathematics Grade 10 pg. 236
- Graph papers
- Rulers
- Stopwatch
- Measuring tape
- Calculators
- Master Core Mathematics Grade 10 pg. 238
- Calculators
- Digital resources

- Oral questions - Observation - Written assignments

Measurements and Geometry

Linear Motion - Velocity-time graph
Linear Motion - Interpreting velocity-time graph
Linear Motion - Relative speed of bodies moving in opposite and same directions

By the end of the lesson, the learner should be able to:
- Draw velocity-time graphs from given data tables and descriptions
- Select suitable scales and plot velocity against time accurately
- Connect velocity-time graphs to real-life scenarios such as recording a car's changing speed along a highway or a cyclist accelerating then braking

In groups, learners are guided to:
- Roll a ball along a track, calculate velocity at each interval and record in a table
- Use data tables to draw velocity-time graphs on graph paper
- Draw velocity-time graphs for motions involving acceleration, constant velocity and deceleration and share work

How do we represent changing velocity on a graph?

- Master Core Mathematics Grade 10 pg. 241
- Graph papers
- Rulers
- Stopwatch
- Ball
- Tape measure
- Calculators
- Master Core Mathematics Grade 10 pg. 244
- Calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 248
- Balls

- Oral questions - Observation - Written assignments

Measurements and Geometry
Statistics and Probability

Linear Motion - Relative speed involving delayed departure and passing lengths
Statistics I - Collection of data

By the end of the lesson, the learner should be able to:
- Solve problems on relative speed involving delayed departure, meeting points and passing lengths
- Determine the time and distance at which two bodies meet given different start times or breakdowns
- Relate these problems to real-life situations such as a learner chasing a school bus that left earlier, a truck overtaking a longer vehicle or a train crossing a bridge

In groups, learners are guided to:
- Solve problems involving vehicles leaving at different times and meeting en route
- Calculate the time and distance for one vehicle to catch up with another
- Solve problems involving trains crossing bridges and trucks passing through tunnels and share work

How do we solve problems when moving bodies start at different times or have different lengths?

- Master Core Mathematics Grade 10 pg. 250
- Calculators
- Rulers
- Graph papers
- Digital resources
- Master Core Mathematics Grade 10 pg. 252
- Digital resources
- Charts

- Oral questions - Observation - Written tests

Statistics and Probability

Statistics I - Frequency distribution table for ungrouped data
Frequency distribution table for ungrouped data - Practice

By the end of the lesson, the learner should be able to:
- Identify the components of a frequency distribution table
- Draw a frequency distribution table for ungrouped data using tally marks
- Relate frequency tables to real life situations like recording the number of siblings in a family or shoe sizes in a class

- Discuss the components of a frequency distribution table including data value, tally and frequency columns
- Collect data on the number of siblings each member of the class has
- Organise the data in a frequency distribution table arranging values from smallest to largest
- Share work with other learners in class

How do we organise raw data for easy interpretation?

- Master Core Mathematics Grade 10 pg. 254
- Digital resources
- Rulers
- Master Core Mathematics Grade 10 pg. 256

- Oral questions - Written assignments

Statistics and Probability

Statistics I - Frequency distribution table for grouped data
Statistics I - Mean of ungrouped data
Statistics I - Mode and median of ungrouped data

By the end of the lesson, the learner should be able to:
- Determine the range and suitable class width for a given set of data
- Draw a frequency distribution table for grouped data
- Relate grouped data tables to real life situations such as recording masses of athletes, scores of participants or heights of learners

- Collect marks scored by learners in the last assessment and identify the lowest and highest marks
- Discuss the most suitable class width and organise data into classes
- Count and record how many items fall in each class using tally marks
- Discuss the importance of grouping data and share work with peers

Why is it important to group data into classes?

- Master Core Mathematics Grade 10 pg. 258
- Digital resources
- Rulers
- Master Core Mathematics Grade 10 pg. 260
- Calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 264

- Written assignments - Oral questions - Observation

Statistics and Probability

Statistics I - Mean of grouped data
Statistics I - Mode of grouped data

By the end of the lesson, the learner should be able to:
- Calculate the midpoint of each class in a grouped frequency distribution
- Determine the mean of grouped data using the formula x̄ = Σfx/Σf
- Relate mean of grouped data to real life situations like determining average marks in a Mathematics assessment, average heights of learners or average ages of bus passengers

- Collect marks scored by learners and group them into appropriate classes
- Calculate the midpoint of each class and complete a frequency distribution table with columns for class, midpoint, frequency and fx
- Work out the mean using the formula x̄ = Σfx/Σf
- Share work with other learners in class

How do we calculate the mean when data is grouped into classes?

- Master Core Mathematics Grade 10 pg. 268
- Calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 270

- Written assignments - Oral questions

Statistics and Probability

Statistics I - Median of grouped data
Statistics I - Histograms with equal class width

By the end of the lesson, the learner should be able to:
- Construct a cumulative frequency column for grouped data
- Calculate the median of grouped data using the median formula
- Relate median of grouped data to real life situations like finding the middle age of hospital patients, the median salary of factory workers or the median power consumption of households

- Collect marks scored by learners and group into appropriate classes
- Complete a frequency distribution table with a cumulative frequency column
- Identify the median class and apply the median formula: Median = L + ((N/2 - cf)/f) × i
- Share work with other groups in class

How do we find the middle value when data is grouped into classes?

- Master Core Mathematics Grade 10 pg. 274
- Calculators
- Digital resources
- Master Core Mathematics Grade 10 pg. 278
- Graph papers
- Rulers
- Calculators

- Written assignments - Oral questions

Statistics and Probability

Statistics I - Histograms with unequal class width

By the end of the lesson, the learner should be able to:
- Calculate frequency density for classes with unequal widths
- Draw histograms with unequal class widths using frequency density
- Relate histograms with unequal class widths to real life situations like representing speeds of vehicles recorded at a checkpoint or heights of recruits in varying class intervals

In groups, learners are guided to:
- Discuss why frequency density is used when class widths are not uniform
- Calculate frequency density using the formula: frequency density = frequency ÷ class width
- Draw histograms using frequency density as the height of each bar
- Compare histograms with equal and unequal class widths

How do we draw histograms when classes have different widths?

- Master Core Mathematics Grade 10 pg. 280
- Graph papers
- Rulers
- Calculators

- Written assignments - Observation

Statistics and Probability

Statistics I - Frequency polygons

By the end of the lesson, the learner should be able to:
- Calculate midpoints of classes and plot frequency against midpoints
- Draw frequency polygons for single and comparative data sets
- Relate frequency polygons to real life situations like comparing daily temperatures of two towns, comparing delivery records across months or comparing marks in different subjects

In groups, learners are guided to:
- Calculate the midpoint of each class in a frequency distribution table
- Plot points of frequency against midpoints on graph paper and join them with straight lines
- Extend the polygon by adding imaginary classes at both ends with frequency zero
- Draw two or more frequency polygons on the same axes for comparison

How do we use frequency polygons to compare data sets?

- Master Core Mathematics Grade 10 pg. 282
- Graph papers
- Rulers
- Calculators

- Written assignments - Observation

Statistics and Probability

Statistics I - Interpretation of data from histograms

By the end of the lesson, the learner should be able to:
- Read and extract information from histograms including modal class and frequencies
- Determine the median class and draw a vertical line showing the median on a histogram
- Relate interpretation of histograms to real life situations like analysing ages of people attending a medical camp, marks in assessments or heights of finger millets on a school farm

In groups, learners are guided to:
- Study given histograms and prepare frequency distribution tables from them
- Determine the total number of items, modal frequency and modal class from histograms
- Identify the median class and draw a vertical line to show where the median lies
- Calculate the number of items above or below certain values using the histogram

What information can we extract from a histogram?

- Master Core Mathematics Grade 10 pg. 284
- Graph papers
- Rulers
- Calculators

- Written assignments - Oral questions

Statistics and Probability

Statistics I - Interpretation of data from frequency polygons

By the end of the lesson, the learner should be able to:
- Read and extract information from frequency polygons including modal class and total frequency
- Compare and analyse data from two or more frequency polygons drawn on the same axes
- Relate interpretation of frequency polygons to real life situations like analysing internet data usage by customers, bags of maize delivered by farmers or comparing daily temperatures between two towns

In groups, learners are guided to:
- Study given frequency polygons and determine the total number of items
- Identify the modal class and modal frequency from frequency polygons
- Determine the number of items above or below certain values from frequency polygons
- Compare two frequency polygons on the same axes to draw conclusions about data stability and trends

How do we use frequency polygons to make informed decisions?

- Master Core Mathematics Grade 10 pg. 286
- Graph papers
- Rulers
- Calculators

- Written assignments - Oral questions

Statistics and Probability

Probability I - Experimental probability
Probability I - Range of probability measure

By the end of the lesson, the learner should be able to:
- Define experimental probability and identify trials and outcomes in experiments
- Calculate experimental probability from results of experiments
- Relate experimental probability to real life situations like predicting rainfall days in a month, chances of a team winning based on past results or likelihood of arriving to school on time

- Toss a coin ten times and record the outcome as head or tail
- Carry out experiments such as throwing a die and recording the number on the top face
- Calculate experimental probability using the formula: number of favourable outcomes ÷ total number of trials
- Share findings with other learners in class

How do we use past results to predict future outcomes?

- Master Core Mathematics Grade 10 pg. 286
- Coins
- Dice
- Digital resources
- Master Core Mathematics Grade 10 pg. 289
- Coloured pens

- Oral questions - Observation - Written assignments

Statistics and Probability

Probability I - Probability space

By the end of the lesson, the learner should be able to:
- List the probability space for single and combined events
- Generate probability spaces using tables and lists for coins and dice
- Relate probability spaces to real life situations like listing possible weather outcomes, possible results of tossing two coins or possible outcomes when rolling two dice

In groups, learners are guided to:
- List all possible outcomes when a coin is tossed once and when tossed twice
- Generate the probability space for two dice tossed together using a two-way table
- Make a spinning wheel and list all possible outcomes after spinning
- Record outcomes in a frequency table and share results with peers

How do we list all possible outcomes of an experiment?

- Master Core Mathematics Grade 10 pg. 290
- Coins
- Dice
- Cards
- Spinning wheel

- Written assignments - Oral questions - Observation

Statistics and Probability

Probability I - Mutually exclusive events

By the end of the lesson, the learner should be able to:
- Define mutually exclusive events and identify them in different situations
- Calculate probabilities of mutually exclusive events
- Relate mutually exclusive events to real life situations like choosing between bus or walking to school, voting for one candidate in an election or selecting between STEM and Social Sciences pathways

In groups, learners are guided to:
- Discuss the meaning of mutually exclusive events and why the occurrence of one prevents the other
- Toss a coin once and determine the probability of getting a head or a tail
- Identify real life events that are mutually exclusive such as elections and career pathway choices
- Calculate probabilities where P(A and B) = 0 and P(A or B) = 1

Why can't two mutually exclusive events happen at the same time?

- Master Core Mathematics Grade 10 pg. 293
- Coins
- Marbles
- Digital resources

- Written assignments - Oral questions

Statistics and Probability

Mutually exclusive events - Practice

By the end of the lesson, the learner should be able to:
- Solve problems involving mutually exclusive events with multiple outcomes
- Determine probabilities of selecting items from bags or groups with multiple categories
- Relate mutually exclusive events to real life situations like probability of a traffic light being red, yellow or green, choosing tea or coffee in a cafeteria or selecting a boy or girl from a class

In groups, learners are guided to:
- Calculate the probability of picking specific coloured marbles from a bag containing multiple colours
- Solve problems where probabilities of mutually exclusive events must sum to 1
- Determine unknown probabilities given other probabilities in mutually exclusive scenarios
- Share solutions and compare approaches with peers

How do we calculate probabilities when there are more than two mutually exclusive outcomes?

- Master Core Mathematics Grade 10 pg. 295
- Marbles
- Calculators
- Digital resources

- Written assignments - Oral questions

Statistics and Probability

Probability I - Independent events

By the end of the lesson, the learner should be able to:
- Define independent events and distinguish them from mutually exclusive events
- Calculate the probability of independent events using P(A and B) = P(A) × P(B)
- Relate independent events to real life situations like the probability of two factory machines failing on the same day, a learner being absent while it rains or drawing balls from two separate bags

In groups, learners are guided to:
- Discuss the meaning of independent events where one event does not affect the other
- Toss a coin twice and determine the probability of getting two heads, two tails or a head and a tail
- Calculate probabilities of combined independent events using multiplication
- Solve problems involving independent events from two separate groups

How do we calculate the probability of two events that do not affect each other?

- Master Core Mathematics Grade 10 pg. 296
- Coins
- Dice
- Bags with balls

- Written assignments - Oral questions

Statistics and Probability

Probability I - Addition law of probability
Probability I - Multiplication law of probability

By the end of the lesson, the learner should be able to:
- State and apply the addition law of probability: P(A or B) = P(A) + P(B)
- Calculate the probability of either event occurring in mutually exclusive situations
- Relate addition law to real life situations like the probability of picking either a yellow or white ball from a box, rolling an odd or even number on a die or getting a specific number or a prime number

- Discuss the meaning of 'or' in probability using Junior School knowledge
- Roll a fair die and determine the probability of getting 1 or 2, an odd number or an even number
- Apply the addition law P(A or B) = P(A) + P(B) to solve problems involving mutually exclusive events
- Share work with other learners in class

When do we add probabilities together?

- Master Core Mathematics Grade 10 pg. 298
- Dice
- Balls of different colours
- Calculators
- Master Core Mathematics Grade 10 pg. 299
- Coins
- Fruit baskets

- Written assignments - Oral questions

Statistics and Probability

Probability I - Probability tree diagrams

By the end of the lesson, the learner should be able to:
- Draw probability tree diagrams showing all possible outcomes and their probabilities
- Calculate probabilities of combined events by multiplying along branches of a tree diagram
- Relate tree diagrams to real life situations like drawing coloured pens from a bag, picking counters without replacement or selecting marbles with replacement

In groups, learners are guided to:
- Toss a fair coin twice and draw a tree diagram showing all possible outcomes
- Put coloured pens in a bag, draw one, replace it and draw another, then represent using a tree diagram
- Multiply probabilities along branches to find probabilities of specific outcomes
- Determine probabilities of events such as getting two of the same colour or at least one of a specific colour

How do tree diagrams help us visualise and calculate probabilities?

- Master Core Mathematics Grade 10 pg. 301
- Coins
- Coloured pens
- Marbles
- Bags

- Written assignments - Oral questions - Observation

Statistics and Probability

Probability tree diagrams - Without replacement
Probability tree diagrams - Application to real life

By the end of the lesson, the learner should be able to:
- Draw probability tree diagrams for events without replacement
- Calculate probabilities from tree diagrams where the total number of items changes after each pick
- Relate tree diagrams without replacement to real life situations like drawing balls from a box without returning them, selecting apples from a basket or choosing learners from a class

- Draw probability tree diagrams for picking two items from a bag without replacement noting how probabilities change
- Calculate probabilities of getting same colour, different colour or at least one of a specific colour
- Solve problems involving fractions of groups such as boys and girls with different characteristics
- Share work and compare solutions with other learners

How do probabilities change when items are not replaced?

- Master Core Mathematics Grade 10 pg. 303
- Balls of different colours
- Bags
- Calculators
- Master Core Mathematics Grade 10 pg. 305
- Calculators
- Digital resources
- Coins
- Dice

- Written assignments - Oral questions